In the history of secret sharing schemes many constructions are based on geometric objects. In this paper we investigate generalizations of threshold schemes and related finite geometric structures. In particular, we analyse compartmented and hierarchical schemes, and deduce some more general results, especially bounds for special arcs and novel constructions for conjunctive 2-level and 3-level hierarchical schemes.

中文翻译：

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广义阈值秘密共享和有限几何

在秘密共享方案的历史上，许多构造都是基于几何对象的。在本文中，我们研究了阈值方案和相关有限几何结构的推广。特别是，我们分析了分区和分层方案，并推导出了一些更一般的结果，特别是特殊弧的边界和连接 2 级和 3 级分层方案的新构造。